[spqlios]: rlwe encryption example

Cargo.lock

@@ -803,7 +803,11 @@ name = "spqlios"
 version = "0.1.0"
 dependencies = [
  "bindgen",
+ "criterion",
  "itertools 0.14.0",
+ "rand",
+ "rand_core",
+ "rand_distr",
  "sampling",
 ]
 

spqlios/Cargo.toml

@@ -4,8 +4,16 @@ version = "0.1.0"
 edition = "2021"
 
 [dependencies]
+rand = "0.8.5"
+rand_core = "0.6.4"
 itertools = "0.14.0"
+criterion = "0.5.1"
+rand_distr = "0.4.3"
 sampling = { path = "../sampling" }
 
 [build-dependencies]
 bindgen = "0.71.1"
+
+[[bench]]
+name = "fft"
+harness = false

spqlios/benches/fft.rs

@@ -0,0 +1,69 @@
+use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
+use spqlios::bindings::*;
+use std::ffi::c_void;
+
+fn fft(c: &mut Criterion) {
+    fn forward<'a>(
+        m: u32,
+        log_bound: u32,
+        reim_fft_precomp: *mut spqlios::reim_fft_precomp,
+        a: &'a [i64],
+    ) -> Box<dyn FnMut() + 'a> {
+        unsafe {
+            let buf_a: *mut f64 = reim_fft_precomp_get_buffer(reim_fft_precomp, 0);
+            reim_from_znx64_simple(m as u32, log_bound as u32, buf_a as *mut c_void, a.as_ptr());
+            Box::new(move || reim_fft(reim_fft_precomp, buf_a))
+        }
+    }
+
+    fn backward<'a>(
+        m: u32,
+        log_bound: u32,
+        reim_ifft_precomp: *mut reim_ifft_precomp,
+        a: &'a [i64],
+    ) -> Box<dyn FnMut() + 'a> {
+        Box::new(move || unsafe {
+            let buf_a: *mut f64 = reim_ifft_precomp_get_buffer(reim_ifft_precomp, 0);
+            reim_from_znx64_simple(m as u32, log_bound as u32, buf_a as *mut c_void, a.as_ptr());
+            reim_ifft(reim_ifft_precomp, buf_a);
+        })
+    }
+
+    let q: u64 = 0x1fffffffffe00001u64;
+
+    let mut b: criterion::BenchmarkGroup<'_, criterion::measurement::WallTime> =
+        c.benchmark_group("fft");
+
+    for log_n in 10..17 {
+        let n: usize = 1 << log_n;
+        let m: usize = n >> 1;
+        let log_bound: u32 = 19;
+
+        let mut a: Vec<i64> = vec![i64::default(); n];
+        a.iter_mut().enumerate().for_each(|(i, x)| *x = i as i64);
+
+        unsafe {
+            let reim_fft_precomp: *mut reim_fft_precomp = new_reim_fft_precomp(m as u32, 1);
+            let reim_ifft_precomp: *mut reim_ifft_precomp = new_reim_ifft_precomp(m as u32, 1);
+
+            let runners: [(String, Box<dyn FnMut()>); 2] = [
+                (format!("forward"), {
+                    forward(m as u32, log_bound, reim_fft_precomp, &a)
+                }),
+                (format!("backward"), {
+                    backward(m as u32, log_bound, reim_ifft_precomp, &a)
+                }),
+            ];
+
+            for (name, mut runner) in runners {
+                let id: BenchmarkId = BenchmarkId::new(name, format!("n={}", 1 << log_n));
+                b.bench_with_input(id, &(), |b: &mut criterion::Bencher<'_>, _| {
+                    b.iter(&mut runner)
+                });
+            }
+        }
+    }
+}
+
+criterion_group!(benches, fft,);
+criterion_main!(benches);

spqlios/examples/rlwe_encrypt.rs

@@ -0,0 +1,89 @@
+use itertools::izip;
+use sampling::source::Source;
+use spqlios::module::{Module, FFT64, VECZNXBIG};
+use spqlios::poly::Poly;
+use spqlios::scalar::Scalar;
+
+fn main() {
+    let n: usize = 16;
+    let log_base2k: usize = 15;
+    let prec: usize = 54;
+    let log_scale: usize = 18;
+    let module: Module = Module::new::<FFT64>(n);
+
+    let mut carry: Vec<u8> = vec![0; module.vec_znx_big_normalize_tmp_bytes()];
+
+    let seed: [u8; 32] = [0; 32];
+    let mut source: Source = Source::new(seed);
+
+    let mut res: Poly = Poly::new(n, log_base2k, prec);
+
+    // Allocates a buffer to store DFT(s)
+    module.new_svp_ppol();
+
+    // s <- Z_{-1, 0, 1}[X]/(X^{N}+1)
+    let mut s: Scalar = Scalar::new(n);
+    s.fill_ternary_prob(0.5, &mut source);
+
+    // Buffer to store s in the DFT domain
+    let mut s_ppol: spqlios::module::SVPPOL = module.new_svp_ppol();
+
+    // s_ppol <- DFT(s)
+    module.svp_prepare(&mut s_ppol, &s);
+
+    // a <- Z_{2^prec}[X]/(X^{N}+1)
+    let mut a: Poly = Poly::new(n, log_base2k, prec);
+    a.fill_uniform(&mut source);
+
+    // Scratch space for DFT values
+    let mut buf_dft: spqlios::module::VECZNXDFT = module.new_vec_znx_dft(a.limbs());
+
+    // Applies buf_dft <- s * a
+    module.svp_apply_dft(&mut buf_dft, &s_ppol, &a);
+
+    // Alias scratch space
+    let mut buf_big: spqlios::module::VECZNXBIG = buf_dft.as_vec_znx_big();
+
+    // buf_big <- IDFT(buf_dft) (not normalized)
+    module.vec_znx_idft_tmp_a(&mut buf_big, &mut buf_dft, a.limbs());
+
+    let mut m: Poly = Poly::new(n, log_base2k, prec - log_scale);
+    let mut want: Vec<i64> = vec![0; n];
+    want.iter_mut()
+        .for_each(|x| *x = source.next_u64n(16, 15) as i64);
+
+    // m
+    m.set_i64(&want, 4);
+    m.normalize(&mut carry);
+
+    // buf_big <- m - buf_big
+    module.vec_znx_big_sub_small_a_inplace(&mut buf_big, &m);
+
+    // b <- normalize(buf_big) + e
+    let mut b: Poly = Poly::new(n, log_base2k, prec);
+    module.vec_znx_big_normalize(&mut b, &buf_big, &mut carry);
+    b.add_normal(&mut source, 3.2, 19.0);
+
+    //Decrypt
+
+    // buf_big <- a * s
+    module.svp_apply_dft(&mut buf_dft, &s_ppol, &a);
+    module.vec_znx_idft_tmp_a(&mut buf_big, &mut buf_dft, b.limbs());
+
+    // buf_big <- a * s + b
+    module.vec_znx_big_add_small_inplace(&mut buf_big, &b);
+
+    // res <- normalize(buf_big)
+    module.vec_znx_big_normalize(&mut res, &buf_big, &mut carry);
+
+    // have = m * 2^{log_scale} + e
+    let mut have: Vec<i64> = vec![i64::default(); n];
+    res.get_i64(&mut have);
+
+    let scale: f64 = (1 << log_scale) as f64;
+    izip!(want.iter(), have.iter())
+        .enumerate()
+        .for_each(|(i, (a, b))| {
+            println!("{}: {} {}", i, a, (*b as f64) / scale);
+        })
+}

spqlios/src/lib.rs

@@ -1,5 +1,6 @@
 pub mod module;
 pub mod poly;
+pub mod scalar;
 
 #[allow(
     non_camel_case_types,
@@ -13,3 +14,15 @@ pub mod bindings {
 }
 
 pub use bindings::*;
+
+fn cast_mut_u64_to_mut_u8_slice(data: &mut [u64]) -> &mut [u8] {
+    let ptr: *mut u8 = data.as_mut_ptr() as *mut u8;
+    let len: usize = data.len() * std::mem::size_of::<u64>();
+    unsafe { std::slice::from_raw_parts_mut(ptr, len) }
+}
+
+fn cast_mut_u8_to_mut_i64_slice(data: &mut [u8]) -> &mut [i64] {
+    let ptr: *mut i64 = data.as_mut_ptr() as *mut i64;
+    let len: usize = data.len() / std::mem::size_of::<i64>();
+    unsafe { std::slice::from_raw_parts_mut(ptr, len) }
+}

spqlios/src/mod.rs

@@ -1 +0,0 @@
-pub mod module;

spqlios/src/module.rs

@@ -1,91 +1,268 @@
 use crate::bindings::*;
+use crate::poly::Poly;
+use crate::scalar::Scalar;
 
-pub fn create_module(N: u64, mtype: module_type_t) -> *mut MODULE {
+pub type MODULETYPE = u8;
+pub const FFT64: u8 = 0;
+pub const NTT120: u8 = 1;
+
+pub struct Module(*mut MODULE);
+
+impl Module {
+    // Instantiates a new module.
+    pub fn new<const MODULETYPE: MODULETYPE>(n: usize) -> Self {
         unsafe {
-        let m = new_module_info(N, mtype);
+            let m: *mut module_info_t = new_module_info(n as u64, MODULETYPE as u32);
             if m.is_null() {
-            println!("Failed to create module.");
+                panic!("Failed to create module.");
+            }
+            Self(m)
         }
-        m
     }
-}
 
-#[test]
+    // Prepares a scalar polynomial (1 limb) for a scalar x vector product.
-fn test_new_module_info() {
+    // Method will panic if a.limbs() != 1.
-    let N: u64 = 1024;
+    pub fn svp_prepare(&self, svp_ppol: &mut SVPPOL, a: &Scalar) {
-    let module_ptr: *mut module_info_t = create_module(N, module_type_t_FFT64);
+        unsafe { svp_prepare(self.0, svp_ppol.0, a.as_ptr()) }
-    assert!(!module_ptr.is_null());
+    }
-    println!("{:?}", module_ptr);
-}
 
-#[cfg(test)]
+    // Allocates a scalar-vector-product prepared-poly (SVPPOL).
-mod tests {
+    pub fn new_svp_ppol(&self) -> SVPPOL {
-    use super::*;
+        unsafe { SVPPOL(new_svp_ppol(self.0)) }
-    use std::ffi::c_void;
+    }
-    use std::time::Instant;
-    //use test::Bencher;
 
-    #[test]
+    // Allocates a vector Z[X]/(X^N+1) that stores normalized in the DFT space.
-    fn test_fft() {
+    pub fn new_vec_znx_dft(&self, limbs: usize) -> VECZNXDFT {
-        let log_bound: usize = 19;
+        unsafe { VECZNXDFT(new_vec_znx_dft(self.0, limbs as u64), limbs) }
+    }
 
-        let n: usize = 2048;
+    // Allocates a vector Z[X]/(X^N+1) that stores not normalized values.
-        let m: usize = n >> 1;
+    pub fn new_vec_znx_big(&self, limbs: usize) -> VECZNXBIG {
+        unsafe { VECZNXBIG(new_vec_znx_big(self.0, limbs as u64), limbs) }
+    }
 
-        let mut a: Vec<i64> = vec![i64::default(); n];
+    // Applies a scalar x vector product: res <- a (ppol) x b
-        let mut b: Vec<i64> = vec![i64::default(); n];
+    pub fn svp_apply_dft(&self, c: &mut VECZNXDFT, a: &SVPPOL, b: &Poly) {
-        let mut c: Vec<i64> = vec![i64::default(); n];
+        let limbs: u64 = b.limbs() as u64;
+        assert!(
+            c.limbs() as u64 >= limbs,
+            "invalid c_vector: c_vector.limbs()={} < b.limbs()={}",
+            c.limbs(),
+            limbs
+        );
+        unsafe { svp_apply_dft(self.0, c.0, limbs, a.0, b.as_ptr(), limbs, b.n() as u64) }
+    }
 
-        a.iter_mut().enumerate().for_each(|(i, x)| *x = i as i64);
+    // b <- IDFT(a), uses a as scratch space.
-        b[1] = 1;
+    pub fn vec_znx_idft_tmp_a(&self, b: &mut VECZNXBIG, a: &mut VECZNXDFT, a_limbs: usize) {
+        assert!(
+            b.limbs() >= a_limbs,
+            "invalid c_vector: b_vector.limbs()={} < a_limbs={}",
+            b.limbs(),
+            a_limbs
+        );
+        unsafe { vec_znx_idft_tmp_a(self.0, b.0, a_limbs as u64, a.0, a_limbs as u64) }
+    }
 
-        println!("{:?}", b);
+    // Returns the size of the scratch space for [vec_znx_idft].
+    pub fn vec_znx_idft_tmp_bytes(&self) -> usize {
+        unsafe { vec_znx_idft_tmp_bytes(self.0) as usize }
+    }
 
+    // b <- IDFT(a), scratch space size obtained with [vec_znx_idft_tmp_bytes].
+    pub fn vec_znx_idft(
+        &self,
+        b_vector: &mut VECZNXBIG,
+        a_vector: &mut VECZNXDFT,
+        a_limbs: usize,
+        tmp_bytes: &mut [u8],
+    ) {
+        assert!(
+            b_vector.limbs() >= a_limbs,
+            "invalid c_vector: b_vector.limbs()={} < a_limbs={}",
+            b_vector.limbs(),
+            a_limbs
+        );
+        assert!(
+            a_vector.limbs() >= a_limbs,
+            "invalid c_vector: c_vector.limbs()={} < a_limbs={}",
+            a_vector.limbs(),
+            a_limbs
+        );
+        assert!(
+            tmp_bytes.len() <= self.vec_znx_idft_tmp_bytes(),
+            "invalid tmp_bytes: tmp_bytes.len()={} < self.vec_znx_idft_tmp_bytes()={}",
+            tmp_bytes.len(),
+            self.vec_znx_idft_tmp_bytes()
+        );
         unsafe {
-            let reim_fft_precomp = new_reim_fft_precomp(m as u32, 2);
+            vec_znx_idft(
-            let reim_ifft_precomp = new_reim_ifft_precomp(m as u32, 1);
+                self.0,
-
+                b_vector.0,
-            let buf_a = reim_fft_precomp_get_buffer(reim_fft_precomp, 0);
+                a_limbs as u64,
-            let buf_b = reim_fft_precomp_get_buffer(reim_fft_precomp, 1);
+                a_vector.0,
-            let buf_c = reim_ifft_precomp_get_buffer(reim_ifft_precomp, 0);
+                a_limbs as u64,
-
+                tmp_bytes.as_mut_ptr(),
-            let now = Instant::now();
-            (0..1024).for_each(|i| {
-                reim_from_znx64_simple(
-                    m as u32,
-                    log_bound as u32,
-                    buf_a as *mut c_void,
-                    a.as_ptr(),
-                );
-                reim_fft(reim_fft_precomp, buf_a);
-
-                reim_from_znx64_simple(
-                    m as u32,
-                    log_bound as u32,
-                    buf_b as *mut c_void,
-                    b.as_ptr(),
-                );
-                reim_fft(reim_fft_precomp, buf_b);
-
-                reim_fftvec_mul_simple(
-                    m as u32,
-                    buf_c as *mut c_void,
-                    buf_a as *mut c_void,
-                    buf_b as *mut c_void,
-                );
-                reim_ifft(reim_ifft_precomp, buf_c);
-
-                reim_to_znx64_simple(
-                    m as u32,
-                    m as f64,
-                    log_bound as u32,
-                    c.as_mut_ptr(),
-                    buf_c as *mut c_void,
             )
-            });
+        }
+    }
 
-            println!("time: {}us", now.elapsed().as_micros());
+    // c <- b - a
-            println!("{:?}", &c[..16]);
+    pub fn vec_znx_big_sub_small_a(&self, c: &mut VECZNXBIG, a: &Poly, b: &VECZNXBIG) {
+        let limbs: usize = a.limbs();
+        assert!(
+            b.limbs() >= limbs,
+            "invalid c: b.limbs()={} < a.limbs()={}",
+            b.limbs(),
+            limbs
+        );
+        assert!(
+            c.limbs() >= limbs,
+            "invalid c: c.limbs()={} < a.limbs()={}",
+            c.limbs(),
+            limbs
+        );
+        unsafe {
+            vec_znx_big_sub_small_a(
+                self.0,
+                c.0,
+                c.limbs() as u64,
+                a.as_ptr(),
+                limbs as u64,
+                a.n() as u64,
+                b.0,
+                b.limbs() as u64,
+            )
+        }
+    }
+
+    // b <- b - a
+    pub fn vec_znx_big_sub_small_a_inplace(&self, b: &mut VECZNXBIG, a: &Poly) {
+        let limbs: usize = a.limbs();
+        assert!(
+            b.limbs() >= limbs,
+            "invalid c_vector: b.limbs()={} < a.limbs()={}",
+            b.limbs(),
+            limbs
+        );
+        unsafe {
+            vec_znx_big_sub_small_a(
+                self.0,
+                b.0,
+                b.limbs() as u64,
+                a.as_ptr(),
+                limbs as u64,
+                a.n() as u64,
+                b.0,
+                b.limbs() as u64,
+            )
+        }
+    }
+
+    // c <- b + a
+    pub fn vec_znx_big_add_small(&self, c: &mut VECZNXBIG, a: &Poly, b: &VECZNXBIG) {
+        let limbs: usize = a.limbs();
+        assert!(
+            b.limbs() >= limbs,
+            "invalid c: b.limbs()={} < a.limbs()={}",
+            b.limbs(),
+            limbs
+        );
+        assert!(
+            c.limbs() >= limbs,
+            "invalid c: c.limbs()={} < a.limbs()={}",
+            c.limbs(),
+            limbs
+        );
+        unsafe {
+            vec_znx_big_add_small(
+                self.0,
+                c.0,
+                limbs as u64,
+                b.0,
+                limbs as u64,
+                a.as_ptr(),
+                limbs as u64,
+                a.n() as u64,
+            )
+        }
+    }
+
+    // b <- b + a
+    pub fn vec_znx_big_add_small_inplace(&self, b: &mut VECZNXBIG, a: &Poly) {
+        let limbs: usize = a.limbs();
+        assert!(
+            b.limbs() >= limbs,
+            "invalid c_vector: b.limbs()={} < a.limbs()={}",
+            b.limbs(),
+            limbs
+        );
+        unsafe {
+            vec_znx_big_add_small(
+                self.0,
+                b.0,
+                limbs as u64,
+                b.0,
+                limbs as u64,
+                a.as_ptr(),
+                limbs as u64,
+                a.n() as u64,
+            )
+        }
+    }
+
+    pub fn vec_znx_big_normalize_tmp_bytes(&self) -> usize {
+        unsafe { vec_znx_big_normalize_base2k_tmp_bytes(self.0) as usize }
+    }
+
+    // b <- normalize(a)
+    pub fn vec_znx_big_normalize(&self, b: &mut Poly, a: &VECZNXBIG, tmp_bytes: &mut [u8]) {
+        let limbs: usize = b.limbs();
+        assert!(
+            b.limbs() >= limbs,
+            "invalid c_vector: b.limbs()={} < a.limbs()={}",
+            b.limbs(),
+            limbs
+        );
+        assert!(
+            tmp_bytes.len() <= self.vec_znx_big_normalize_tmp_bytes(),
+            "invalid tmp_bytes: tmp_bytes.len()={} <= self.vec_znx_big_normalize_tmp_bytes()={}",
+            tmp_bytes.len(),
+            self.vec_znx_big_normalize_tmp_bytes()
+        );
+        unsafe {
+            vec_znx_big_normalize_base2k(
+                self.0,
+                b.log_base2k as u64,
+                b.as_mut_ptr(),
+                limbs as u64,
+                b.n() as u64,
+                a.0,
+                limbs as u64,
+                tmp_bytes.as_mut_ptr(),
+            )
         }
     }
 }
+
+pub struct SVPPOL(*mut svp_ppol_t);
+pub struct VECZNXDFT(*mut vec_znx_dft_t, usize);
+pub struct VECZNXBIG(*mut vec_znx_bigcoeff_t, usize);
+
+impl VECZNXBIG {
+    pub fn as_vec_znx_dft(&mut self) -> VECZNXDFT {
+        VECZNXDFT(self.0 as *mut vec_znx_dft_t, self.1)
+    }
+    pub fn limbs(&self) -> usize {
+        self.1
+    }
+}
+
+impl VECZNXDFT {
+    pub fn as_vec_znx_big(&mut self) -> VECZNXBIG {
+        VECZNXBIG(self.0 as *mut vec_znx_bigcoeff_t, self.1)
+    }
+    pub fn limbs(&self) -> usize {
+        self.1
+    }
+}

spqlios/src/poly.rs

@@ -1,46 +1,51 @@
-use crate::{znx_normalize, znx_zero_i64_ref};
+use crate::{
+    cast_mut_u8_to_mut_i64_slice, znx_automorphism_i64, znx_automorphism_inplace_i64,
+    znx_normalize, znx_zero_i64_ref,
+};
 use itertools::izip;
+use rand_distr::{Distribution, Normal};
+use sampling::source::Source;
 use std::cmp::min;
 
 pub struct Poly {
     pub n: usize,
-    pub k: usize,
+    pub log_base2k: usize,
     pub prec: usize,
     pub data: Vec<i64>,
 }
 
 impl Poly {
-    pub fn new(n: usize, k: usize, prec: usize) -> Self {
+    pub fn new(n: usize, log_base2k: usize, prec: usize) -> Self {
         Self {
             n: n,
-            k: k,
+            log_base2k: log_base2k,
             prec: prec,
-            data: vec![i64::default(); Self::buffer_size(n, k, prec)],
+            data: vec![i64::default(); Self::buffer_size(n, log_base2k, prec)],
         }
     }
 
-    pub fn buffer_size(n: usize, k: usize, prec: usize) -> usize {
+    pub fn buffer_size(n: usize, log_base2k: usize, prec: usize) -> usize {
-        n * ((prec + k - 1) / k)
+        n * ((prec + log_base2k - 1) / log_base2k)
     }
 
-    pub fn from_buffer(&mut self, n: usize, k: usize, prec: usize, buf: &[i64]) {
+    pub fn from_buffer(&mut self, n: usize, log_base2k: usize, prec: usize, buf: &[i64]) {
-        let size = Self::buffer_size(n, k, prec);
+        let size = Self::buffer_size(n, log_base2k, prec);
         assert!(
             buf.len() >= size,
             "invalid buffer: buf.len()={} < self.buffer_size(n={}, k={}, prec={})={}",
             buf.len(),
             n,
-            k,
+            log_base2k,
             prec,
             size
         );
         self.n = n;
-        self.k = k;
+        self.log_base2k = log_base2k;
         self.prec = prec;
         self.data = Vec::from(&buf[..size])
     }
 
-    pub fn log_n(&self) -> usize {
+    pub fn log_n(&self) -> u64 {
         (u64::BITS - (self.n - 1).leading_zeros()) as _
     }
 
@@ -48,10 +53,22 @@ impl Poly {
         self.n
     }
 
+    pub fn prec(&self) -> usize {
+        self.prec
+    }
+
     pub fn limbs(&self) -> usize {
         self.data.len() / self.n
     }
 
+    pub fn as_ptr(&self) -> *const i64 {
+        self.data.as_ptr()
+    }
+
+    pub fn as_mut_ptr(&mut self) -> *mut i64 {
+        self.data.as_mut_ptr()
+    }
+
     pub fn at(&self, i: usize) -> &[i64] {
         &self.data[i * self.n..(i + 1) * self.n]
     }
@@ -70,54 +87,57 @@ impl Poly {
 
     pub fn set_i64(&mut self, data: &[i64], log_max: usize) {
         let size: usize = min(data.len(), self.n());
-        let k_rem: usize = self.k - (self.prec % self.k);
+        let k_rem: usize = self.log_base2k - (self.prec % self.log_base2k);
 
-        // If 2^{base} * 2^{k_rem} < 2^{63}-1, then we can simply copy
+        // If 2^{log_base2k} * 2^{k_rem} < 2^{63}-1, then we can simply copy
         // values on the last limb.
-        // Else we decompose values base k.
+        // Else we decompose values base2k.
-        if log_max + k_rem < 63 || k_rem == self.k {
+        if log_max + k_rem < 63 || k_rem == self.log_base2k {
             self.at_mut(self.limbs() - 1).copy_from_slice(&data[..size]);
         } else {
-            let mask: i64 = (1 << self.k) - 1;
+            let mask: i64 = (1 << self.log_base2k) - 1;
             let limbs = self.limbs();
-            let steps: usize = min(limbs, (log_max + k_rem + self.k - 1) / self.k);
+            let steps: usize = min(limbs, (log_max + self.log_base2k - 1) / self.log_base2k);
             (limbs - steps..limbs)
                 .rev()
                 .enumerate()
                 .for_each(|(i, i_rev)| {
-                    let shift: usize = i * self.k;
+                    let shift: usize = i * self.log_base2k;
                     izip!(self.at_mut(i_rev)[..size].iter_mut(), data[..size].iter())
                         .for_each(|(y, x)| *y = (x >> shift) & mask);
                 })
         }
 
         // Case where self.prec % self.k != 0.
-        if k_rem != self.k {
+        if k_rem != self.log_base2k {
             let limbs = self.limbs();
-            let steps: usize = min(limbs, (log_max + k_rem + self.k - 1) / self.k);
+            let steps: usize = min(limbs, (log_max + self.log_base2k - 1) / self.log_base2k);
             (limbs - steps..limbs).rev().for_each(|i| {
                 self.at_mut(i)[..size].iter_mut().for_each(|x| *x <<= k_rem);
             })
         }
     }
 
-    pub fn normalize(&mut self, carry: &mut [i64]) {
+    pub fn normalize(&mut self, carry: &mut [u8]) {
         assert!(
-            carry.len() >= self.n,
+            carry.len() >= self.n * 8,
             "invalid carry: carry.len()={} < self.n()={}",
             carry.len(),
             self.n()
         );
+
+        let carry_i64: &mut [i64] = cast_mut_u8_to_mut_i64_slice(carry);
+
         unsafe {
-            znx_zero_i64_ref(self.n() as u64, carry.as_mut_ptr());
+            znx_zero_i64_ref(self.n() as u64, carry_i64.as_mut_ptr());
             (0..self.limbs()).rev().for_each(|i| {
                 znx_normalize(
                     self.n as u64,
-                    self.k as u64,
+                    self.log_base2k as u64,
                     self.at_mut_ptr(i),
-                    carry.as_mut_ptr(),
+                    carry_i64.as_mut_ptr(),
                     self.at_mut_ptr(i),
-                    carry.as_mut_ptr(),
+                    carry_i64.as_mut_ptr(),
                 )
             });
         }
@@ -131,20 +151,111 @@ impl Poly {
             self.n
         );
         data.copy_from_slice(self.at(0));
-        let rem: usize = self.k - (self.prec % self.k);
+        let rem: usize = self.log_base2k - (self.prec % self.log_base2k);
         (1..self.limbs()).for_each(|i| {
-            if i == self.limbs() - 1 && rem != self.k {
+            if i == self.limbs() - 1 && rem != self.log_base2k {
-                let k_rem: usize = self.k - rem;
+                let k_rem: usize = self.log_base2k - rem;
                 izip!(self.at(i).iter(), data.iter_mut()).for_each(|(x, y)| {
                     *y = (*y << k_rem) + (x >> rem);
                 });
             } else {
                 izip!(self.at(i).iter(), data.iter_mut()).for_each(|(x, y)| {
-                    *y = (*y << self.k) + x;
+                    *y = (*y << self.log_base2k) + x;
                 });
             }
         })
     }
+
+    pub fn automorphism_inplace(&mut self, gal_el: i64) {
+        unsafe {
+            (0..self.limbs()).for_each(|i| {
+                znx_automorphism_inplace_i64(self.n as u64, gal_el, self.at_mut_ptr(i))
+            })
+        }
+    }
+    pub fn automorphism(&mut self, gal_el: i64, a: &mut Poly) {
+        unsafe {
+            (0..self.limbs()).for_each(|i| {
+                znx_automorphism_i64(self.n as u64, gal_el, a.at_mut_ptr(i), self.at_ptr(i))
+            })
+        }
+    }
+
+    pub fn fill_uniform(&mut self, source: &mut Source) {
+        let mut base2k: u64 = 1 << self.log_base2k;
+        let mut mask: u64 = base2k - 1;
+        let mut base2k_half: i64 = (base2k >> 1) as i64;
+
+        let size: usize = self.n() * (self.limbs() - 1);
+
+        self.data[..size]
+            .iter_mut()
+            .for_each(|x| *x = (source.next_u64n(base2k, mask) as i64) - base2k_half);
+
+        let log_base2k_rem: usize = self.prec % self.log_base2k;
+
+        if log_base2k_rem != 0 {
+            base2k = 1 << log_base2k_rem;
+            mask = (base2k - 1) << (self.log_base2k - log_base2k_rem);
+            base2k_half = ((mask >> 1) + 1) as i64;
+        }
+
+        self.data[size..]
+            .iter_mut()
+            .for_each(|x| *x = (source.next_u64n(base2k, mask) as i64) - base2k_half);
+    }
+
+    pub fn add_dist_f64<T: Distribution<f64>>(&mut self, source: &mut Source, dist: T, bound: f64) {
+        let log_base2k_rem: usize = self.prec % self.log_base2k;
+
+        if log_base2k_rem != 0 {
+            self.at_mut(self.limbs() - 1).iter_mut().for_each(|a| {
+                let mut dist_f64: f64 = dist.sample(source);
+                while dist_f64.abs() > bound {
+                    dist_f64 = dist.sample(source)
+                }
+                *a += (dist_f64.round() as i64) << log_base2k_rem
+            });
+        } else {
+            self.at_mut(self.limbs() - 1).iter_mut().for_each(|a| {
+                let mut dist_f64: f64 = dist.sample(source);
+                while dist_f64.abs() > bound {
+                    dist_f64 = dist.sample(source)
+                }
+                *a += dist_f64.round() as i64
+            });
+        }
+    }
+
+    pub fn add_normal(&mut self, source: &mut Source, sigma: f64, bound: f64) {
+        self.add_dist_f64(source, Normal::new(0.0, sigma).unwrap(), bound);
+    }
+
+    pub fn trunc_pow2(&mut self, k: usize) {
+        if k == 0 {
+            return;
+        }
+
+        assert!(
+            k <= self.prec,
+            "invalid argument k: k={} > self.prec()={}",
+            k,
+            self.prec()
+        );
+
+        self.prec -= k;
+        self.data
+            .truncate((self.limbs() - k / self.log_base2k) * self.n());
+
+        let k_rem: usize = k % self.log_base2k;
+
+        if k_rem != 0 {
+            let mask: i64 = ((1 << (self.log_base2k - k_rem - 1)) - 1) << k_rem;
+            self.at_mut(self.limbs() - 1)
+                .iter_mut()
+                .for_each(|x: &mut i64| *x &= mask)
+        }
+    }
 }
 
 #[cfg(test)]
@@ -171,9 +282,9 @@ mod tests {
 
     #[test]
     fn test_set_get_i64_hi_norm() {
-        let n: usize = 1;
+        let n: usize = 8;
-        let k: usize = 19;
+        let k: usize = 17;
-        let prec: usize = 128;
+        let prec: usize = 84;
         let mut a: Poly = Poly::new(n, k, prec);
         let mut have: Vec<i64> = vec![i64::default(); n];
         let mut source = Source::new([1; 32]);
@@ -183,8 +294,35 @@ mod tests {
                 .wrapping_sub(u64::MAX / 2 + 1) as i64;
         });
         a.set_i64(&have, 63);
+        //(0..a.limbs()).for_each(|i| println!("i:{} -> {:?}", i, a.at(i)));
+        let mut want = vec![i64::default(); n];
+        //(0..a.limbs()).for_each(|i| println!("i:{} -> {:?}", i, a.at(i)));
+        a.get_i64(&mut want);
+        izip!(want, have).for_each(|(a, b)| assert_eq!(a, b, "{} != {}", a, b));
+    }
+    #[test]
+    fn test_normalize() {
+        let n: usize = 8;
+        let k: usize = 17;
+        let prec: usize = 84;
+        let mut a: Poly = Poly::new(n, k, prec);
+        let mut have: Vec<i64> = vec![i64::default(); n];
+        let mut source = Source::new([1; 32]);
+        have.iter_mut().for_each(|x| {
+            *x = source
+                .next_u64n(u64::MAX, u64::MAX)
+                .wrapping_sub(u64::MAX / 2 + 1) as i64;
+        });
+        a.set_i64(&have, 63);
+        let mut carry: Vec<u8> = vec![u8::default(); n * 8];
+        a.normalize(&mut carry);
+
+        let base_half = 1 << (k - 1);
+        a.data
+            .iter()
+            .for_each(|x| assert!(x.abs() <= base_half, "|x|={} > 2^(k-1)={}", x, base_half));
         let mut want = vec![i64::default(); n];
         a.get_i64(&mut want);
-        izip!(want, have).for_each(|(a, b)| assert_eq!(a, b));
+        izip!(want, have).for_each(|(a, b)| assert_eq!(a, b, "{} != {}", a, b));
     }
 }

spqlios/src/scalar.rs

@@ -0,0 +1,48 @@
+use rand::distributions::{Distribution, WeightedIndex};
+use rand::seq::SliceRandom;
+use rand_core::RngCore;
+use sampling::source::Source;
+
+pub struct Scalar(pub Vec<i64>);
+
+impl Scalar {
+    pub fn new(n: usize) -> Self {
+        Self(vec![i64::default(); Self::buffer_size(n)])
+    }
+
+    pub fn buffer_size(n: usize) -> usize {
+        n
+    }
+
+    pub fn from_buffer(&mut self, n: usize, buf: &[i64]) {
+        let size = Self::buffer_size(n);
+        assert!(
+            buf.len() >= size,
+            "invalid buffer: buf.len()={} < self.buffer_size(n={})={}",
+            buf.len(),
+            n,
+            size
+        );
+        self.0 = Vec::from(&buf[..size])
+    }
+
+    pub fn as_ptr(&self) -> *const i64 {
+        self.0.as_ptr()
+    }
+
+    pub fn fill_ternary_prob(&mut self, prob: f64, source: &mut Source) {
+        let choices: [i64; 3] = [-1, 0, 1];
+        let weights: [f64; 3] = [prob / 2.0, 1.0 - prob, prob / 2.0];
+        let dist: WeightedIndex<f64> = WeightedIndex::new(&weights).unwrap();
+        self.0
+            .iter_mut()
+            .for_each(|x: &mut i64| *x = choices[dist.sample(source)]);
+    }
+
+    pub fn fill_ternary_hw(&mut self, hw: usize, source: &mut Source) {
+        self.0[..hw]
+            .iter_mut()
+            .for_each(|x: &mut i64| *x = (((source.next_u32() & 1) as i64) << 1) - 1);
+        self.0.shuffle(source);
+    }
+}

spqlios/tests/module.rs

@@ -1,9 +0,0 @@
-use spqlios::bindings::{module_info_t, module_type_t_FFT64};
-use spqlios::module::create_module;
-
-#[test]
-fn test_new_module_info() {
-    let N: u64 = 1024;
-    let module_ptr: *mut module_info_t = create_module(N, module_type_t_FFT64);
-    assert!(!module_ptr.is_null());
-}